Neat epoxy resin (EP) is a highly flammable material, and the pyrolysis volatiles of it contain some harmful gases such as carbon monoxide, aromatic compounds, hydrocarbons, etc. Herein, an organic–inorganic hybrid named ethanediamine-modified ammonium polyphosphate (EDA-APP) was used to prepare monocomponent intumescent flame-retardant EP composites. Cu₂O was used as a synergist for the EP/EDA-APP system. The fire behavior and smoke emission of EP composites were evaluated by limiting oxygen index (LOI), UL-94 vertical burning, and cone calorimeter test. The results show that the minimum demand of EDA-APP (21 wt%) is lower than that of APP (25 wt%) to obtain a UL-94 V-0 rating. In addition, the contents of EDA-APP can be further reduced to 16.3 wt% to reach UL-94 V-0, and a high LOI value of 31% can be obtained only via the addition of extra 1.7 wt% Cu₂O. Interestingly, the total smoke production (TSP) and carbon monoxide production (COP) are further decreased by loading Cu₂O onto the EP/EDA-APP composite. Then, the thermal decomposition behavior, morphology, and composition of EP composites and their condensed and gaseous pyrolysis products were analyzed by thermogravimetric analysis (TGA), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and energy-dispersive X-ray (EDX) spectroscopy, respectively. The test results revealed that the enhancement in flame retardancy and smoke suppression of EP/EDA-APP/Cu₂O is due to the synergistic effect and catalytic action of Cu₂O for accelerating the char formation rate and improving the formation amount, intumescent degree, and compactness of char.